Five members of a Bangladeshi family living at the Grenfell Tower remain missing more than a day after flames tore through the 24-storey building in west London, killing at least 17 people.

There has been no trace of Kamru Miah, his wife, and their three children, who got trapped at their 16th-floor apartment early Wednesday, said Kamru's nephew Abdur Rahim who lives in London.

Rahim said he had talked to Kamru and his wife Hasna Begum Tanya over the phone around 2:30am on Wednesday for the last time.

Tanya told him that the family members were desperately looking for help, and that they were trying to escape through a bathroom of the apartment but were unable to find a way out. She also asked him to pray for them.

After that, Rahim found the mobile phones of the couple switched off.

Ninety-year-old Kamru moved to the Grenfell Tower with his wife, sons Abdul Hamid and Abdul Hanif, and daughter Tanima only a year ago.

His another son, Abdul Hakim, lives at a different place in the UK.

Police haven't yet been able to provide any information on them.

Talking to this correspondent yesterday, Kamru's eldest son Sujon Miah, who lives in Moulvibazar's Koishaura village, said he had been unable to reach his parents and the three siblings over the phone since Wednesday morning.

He said his sister Tanima was to get married on 29th July, and that she had already done shopping and completed all preparations for her wedding.

Contacted, Khondker M Talha, Bangladesh deputy high commissioner in London, said, “We are in contact with police, emergency services and the [Bangladeshi] community … We will let you know.”

Meanwhile, British Prime Minister Theresa May promised a public enquiry into the fire, as the government faced questions about how such a devastating blaze could have occurred, reports Reuters.

Smoke was still wafting out of the blackened shell of the Grenfell Tower yesterday where specialist search teams faced hazardous conditions as they scoured the wreck, with external cladding still falling from the building.

Fire engulfed the social housing block, where as many as 600 people lived in more than 120 apartments, in the early hours of Wednesday, turning it into a flaming torch in minutes.

"Sadly I can confirm that the number of people that have died is now 17," London Police Commander Stuart Cundy told reporters.

He said that number was expected to rise and firefighters have said they did not expect to find any more survivors after rescuing 65. Thirty-seven people remained in hospital, with 17 of them in critical care.

"Our absolute priority for all of us is identifying and locating those people who are still missing," Cundy said before declining to comment on speculation about the likely final death toll.

An investigation into the cause of the blaze, the worst in the British capital in a generation, was underway. But the shock at its scale turned to anger and recriminations.

Opponents of May's government demanded to know whether more could have been done to prevent the disaster and if spending cuts to local authorities had played a part.

May visited the scene yesterday to meet members of the emergency services.

"Right now, people want answers and it's absolutely right and that's why I am today ordering a full public inquiry into this disaster." she said

"We need to know what happened, we need to have an explanation of this. People deserve answers; the inquiry will give them."

Local residents say there had been repeated warnings about the safety of the building, which recently underwent an 8.7 million pound ($11.1 million) exterior refurbishment, including new external cladding and windows.

Planning documents detailing the refurbishment did not refer to a type of fire barrier that building safety experts said should be used when high-rise blocks are being re-clad, according to Reuters research.

The government has also promised that other tower blocks which were also recently refurbished would be assessed.

"We have to get to the bottom of this. The truth has got to come out, and it will," opposition Labour leader Jeremy Corbyn said as he visited volunteers at the site.

London Fire Brigade chief Dany Cotton, who said the fire had been unprecedented in its scale, said urban search units backed by specialist dog teams would slowly make their way through the building as structural surveyors helped make the tower safe.

Survivors, who lost their belongings in the blaze, spent the night at emergency shelters, as charities and local support groups were flooded with donations of clothes and bedding from shocked Londoners.

Many were seeking news of the missing. Semira Mohammed, 37, a science technician who lives nearby, said she knew a family of five who lived on the 21st floor of the block.

"I kept calling and calling," she told Reuters. "The phone was ringing but they didn't reply to us. We were from the same community, and many in the tower were. Maybe 70 percent are from Somalia, Sudan, Morocco, and she was so happy to be in the flat right in that community."

The Syrian Solidarity Campaign said on its Facebook webpage that Mohammed Al Haj Ali, a refugee from Syria, was one of those who had been killed.

The tower, built in 1974 on the low-rent housing estate in North Kensington, sits in a part of west London surrounded by some of the most affluent areas of the capital.